A random number generator gives results that are uniformly distributed with a minimum of 43 and a maximum of 70. What is the probability that a random number is between 45 and 58?
Solution :
Given that,
a = 43
b = 70
P(c < x < d) = (d - c) / (b - a)
P(45< x < 58) = (58 - 45) / (70 - 43)=0.4815
probability=0.4815
A random number generator gives results that are uniformly distributed with a minimum of 43 and...
The time to fly between New York City and Chicago is uniformly distributed with a minimum of 90 minutes and a maximum of 150 minutes. What is the probability that a flight is more than 140 minutes?
Problem 2. Suppose that a uniformly distributed random number X in [0, 1] is found by calling a random number generator. Then, if the call to the RNG produces the value r for X, another random number Y is computed that is uniformly distributed on (0, x). That is, X is uniform on the interval [0, 1], and the conditional distribution for Y given X -a is uniform on the interval [0,x] a) Calculate E(Y X-0.4). b) Calculate E (X...
A coder programmed a random number generator, which generates a random number between 0 and 1 when the user presses the "random" button. Numbers generated follow a uniform distribution. 12- What is the probability the next time the button is pressed the code will generate a number less than .23? 13- What is the probability the next time the button is pressed the code will generate a number between .23 and .35? 14- What is the probability the next time...
Problem 5. Suppose that a uniformly distributed random number X in 0 is found by calling a random number generator. Then, if the call to the RNG pro- duces the value r for X, another random umber Y is computed that is uniformly distributed on 0, . That is, X is uniform on the interval 0,1], and the conditional distribution for Y given X = 1 is uniform on the interval [0.11 a) Give fonmulas for E(Y X) and Var(Y...
Let Ui and U2 be independent random variables, each one distributed uniformly on Z be the minimum, Z = min{U1, U2} and W be the maximum, W = max{U1, U2}. Find the joint p.d.f of Z and W [0, 1]. Let
Let Ui and U2 be independent random variables, each one distributed uniformly on Z be the minimum, Z = min{U1, U2} and W be the maximum, W = max{U1, U2}. Find the joint p.d.f of Z and W [0,...
Independent random sampling from two normally distributed populations gives the results below. Find a 99% confidence interval estimate of the difference between the means of the two populations ni 70 X1-377 ƠI :19 n2-34 x2 334 ơ2-29 The confidence interval is < (m-μ2) (Round to four decimal places as needed)
A random number generator will spread its output uniformly across the entire interval from 0 to 1 as we allow it to generate a long sequence of numbers. The results of many trials are represented by the density curve of a uniform distribution. This density curve appears in red in the given figure. It has height 1 over the interval from 0 to 1, and height 0 everywhere else. The area under the density curve is 1: the area of...
Assume that x is a uniformly distributed random number between 0 and 1 (e.g. x is the RAND() function in Excel), and that the number of units to be sold is uniformly distributed between 100 and 400. In this case, sales are given by the expression: 400 - 100 * x 100 + 400 * x 400 + x 300 + / - x
5. S distribution. uppose that exam grades are Uniformly distributed between 60 a nd 100. Assume a continuous a) what is the probability that a student selected at random made between 70 and 90? b) What is the probability that a student selected at random made between a 40 and 70? c) What is the probability that a student selected at random made above a 70? d) What is the probability that a student selected at random made exactly an...
A continuous random variable is uniformly distributed between 0 and 96. What is the probability a random draw from this distribution will be on the closed interval between 39 and 75? Enter your answer as a decimal to 3 decimal places.